Page 102 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

84 Thomas Russell et al.

Which of the two minima should be used is still a matter of some
contention. Some authors suggest that the electrostatic force experienced
when leaving the primary minimum is too great for any other forces to
detach the particle; hence, all particles that can detach must have resided
in the secondary minimum. On the other hand, as outlined in the low-
salinity curve in Fig. 3.6, some potential energy profiles either do not
have secondary minima, or they are too small to prevent particles from
freely leaving due to Brownian motion (Bradford et al., 2013).
Calculations for gravitational and lift forces indicate that their order of
magnitude range is between 10 214 and 10 213 , although drag and electro-
211 28
static forces range between 10 and 10 (Bedrikovetsky et al., 2012;
Kalantariasl and Bedrikovetsky, 2013). Therefore, gravitational and lift
forces are disregarded and only drag and electrostatic forces are considered
to be relevant to determine conditions for particle detachment.
Calculations of the torque balance will only take into account drag and
electrostatic forces and thus, Eq. (3.1) simplifies to the following form:

ð
F d U; r s Þ 5 F e r s ; γ; pH; Tð Þlr s ; F e Þ; (3.15)
ð
Favorable conditions for particle mobilization happen when the drag
torque exceeds the electrostatic torque. If the particle is attached to the
pore surface, this means that it is in a stable equilibrium, where the net
force on the particle is zero.
The equations for lever arms, drag, and electrostatic forces provide an
understanding of which parameters can lead to favorable conditions for
particle detachment during waterflooding. The drag force is mainly a
function of velocity and particle size. The higher the carrier fluid velocity
and particle size, the higher the drag force, increasing the likelihood of
particle detachment. The electrostatic force is primarily affected by water
salinity, pH, and temperature. The attractive London-Van der Waals
potential and repulsive Born potential are functions of the Hamaker
constant, which is a function of the dielectric constant and refractive
index for particle, grain, and fluid, both are temperature dependent
(Israelachvili, 2011). An increase in the temperature will increase repul-
sion between the particle and surface. The repulsive electrical double
layer is a function of the inverse Debye length and zeta potentials. The
first is inversely proportional to the water salinity and pH, meaning that
lower salinity and higher pH will lead to higher repulsion between parti-
cle and surface. The second is a function of pH and temperature, higher
pH and temperature will also lead to stronger repulsion. Thus, high pH